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On the perturbative expansion at high temperature and implications for cosmological phase transitions

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arxiv 2104.04399 v2 pith:64DKPPYZ submitted 2021-04-09 hep-ph astro-ph.COgr-qchep-th

On the perturbative expansion at high temperature and implications for cosmological phase transitions

classification hep-ph astro-ph.COgr-qchep-th
keywords temperaturehighrenormalisationscaleeffectiveexpansionperturbativephase
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We revisit the perturbative expansion at high temperature and investigate its convergence by inspecting the renormalisation scale dependence of the effective potential. Although at zero temperature the renormalisation group improved effective potential is scale independent at one-loop, we show how this breaks down at high temperature, due to the misalignment of loop and coupling expansions. Following this, we show how one can recover renormalisation scale independence at high temperature, and that it requires computations at two-loop order. We demonstrate how this resolves some of the huge theoretical uncertainties in the gravitational wave signal of first-order phase transitions, though uncertainties remain stemming from the computation of the bubble nucleation rate.

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